Adaptive hybrid statistical based timing skew estimation method

Abstract

The adaptive mixed statistics based timing offset estimation method belongs to the technical field of multi-channel signal sampling and processing, and particularly relates to a mixed correlation and differential statistics based timing offset estimation and calibration method for a multi-channel sampling system. The method solves the technical problems of structural desensitization near a specific signal frequency point and poor robustness in a noise environment inherent in the single statistics based timing offset estimation method in the prior art. The method comprises driving the relative timing offset estimation value to iteratively update in the mixed error item as the update direction. The adaptive mixed statistics based timing offset estimation method is suitable for occasions requiring background real-time calibration of the inter-channel sampling time offset.

Description

Technical Field

[0001] This invention relates to the field of multi-channel signal sampling and processing technology, and in particular to a time-series deviation estimation method based on adaptive hybrid statistics for multi-channel sampling systems. Background Technology

[0002] Multi-channel sampling systems are widely used in array signal processing, distributed sensing, broadband communication reception, and time-interleaved sampling systems. Ideally, each sampling channel should synchronously or interleave the same continuous time signal according to a predetermined nominal time, thereby achieving multi-channel collaborative processing and information fusion.

[0003] However, in practical systems, due to factors such as clock jitter, channel path mismatch, circuit delay differences, and device manufacturing process variations, there are often sampling time deviations, or timing deviations, between different sampling channels. These timing deviations disrupt the temporal consistency between multi-channel sampling results, leading to a decrease in subsequent processing performance. In time-interleaved sampling systems, timing deviations also introduce significant spurious signals and distortions, affecting the overall system accuracy. Therefore, high-precision timing deviation estimation is crucial for system calibration and performance assurance.

[0004] For estimating timing deviations, existing technical solutions mainly follow two major technical paths:

[0005] The first type of approach relies on known input signals. These methods require applying pilot sequences, specific training waveforms, or known test signals (such as single-frequency tones, sawtooth waves, etc.) to the system input, and then determining the channel delay through correlation peak search, maximum likelihood estimation, or frequency domain fitting. Such methods can achieve high accuracy in controlled laboratory or foreground calibration modes. However, their fundamental drawback lies in severely limited application scenarios: these methods require pre-provided known inputs, making blind estimation difficult under unknown inputs or normal operating conditions; they cannot operate in the "background" state where the system is transmitting normal business data or processing unknown or arbitrary input signals. For communication or monitoring systems that require continuous operation and cannot tolerate interruptions during calibration, these methods lack practicality.

[0006] The second type of approach is the blind estimation method in the background, which is also the mainstream research method currently. This type of method does not rely on any prior knowledge of the input signal; it extracts time-series deviation information solely through statistical analysis of the actual output data of the system, thus possessing greater practical value. Its main technical approach is to construct an error statistic that reflects the time-series deviation and then perform recursive estimation using adaptive filtering algorithms such as least mean square. Depending on the constructed statistic, it can be further divided into two subcategories:

[0007] Methods based on correlation statistics: The core of these methods is calculating the (cross-)correlation between sampled values ​​from adjacent channels, or calculating the product of the compensation error and the local derivative (slope) of the signal. Correlation statistics can reflect the consistency relationship between the error and the local slope. The mathematical expectation of this statistic has a certain functional relationship with the time series deviation (usually approximately linear when the deviation is small), and can be used as the direction of the updated gradient.

[0008] Methods based on differential (or sign-based) statistics: The core of these methods is to combine the sign information of the compensation error with the local trend of signal variation to extract information related to the direction of time-series deviation. Differential statistics can reflect the deviation information between the error sign and the local trend of variation. Unlike processing that only performs simple difference or sign comparison between adjacent sample values, these statistics are usually based on the joint construction of the compensation error and the local slope. These methods are relatively insensitive to the magnitude of the error, focusing more on determining the direction of the deviation.

[0009] While statistical-based backend methods offer structural advantages, most existing techniques still revolve around constructing error-driving terms based on a single statistic and updating them using recursive algorithms such as LMS. The applicant's in-depth research revealed that existing schemes, whether relying solely on correlation-based or difference-based statistics, suffer from a series of inherent and insurmountable flaws that severely limit their performance in complex real-world environments:

[0010] (1) Structural desensitization problem – an inherent defect of single statistics. This is a core technical problem that has long existed in this field but has not been effectively solved. For correlation statistics, their sensitivity (i.e., the rate of change of the expected value of the statistic relative to the time series deviation) is not constant, but a periodic function of the frequency of the input signal. When the frequency of the input signal is close to certain specific integer multiples of the system sampling rate or its components, the sensitivity of the correlation statistics will drop sharply or even theoretically approach zero (desensitization). At this time, the estimation loop loses its effective driving force, resulting in convergence stagnation, increased estimation error variance, or even divergence. Similarly, difference statistics also have their own "concave points" of sensitivity change, only at different frequency points. This performance collapse that inevitably occurs at a specific frequency point due to the nature of the algorithm's mathematical model is called "structural desensitization". It means that no single statistical method can provide stable and reliable estimates across all frequency bands, leading to insufficient estimation driving force, increased error fluctuations, or poor convergence performance.

[0011] (2) The effective information (error information) of different statistics is not fully utilized, failing to form a complementary advantage. Correlation and difference statistics have different response characteristics to frequency, noise, and bias magnitude, and are theoretically complementary. For example, at frequencies where correlation statistics tend to become insensitive, difference statistics may still maintain good sensitivity; under high noise, difference statistics that utilize sign information may be more robust than correlation statistics that are directly multiplied. However, existing techniques usually select only one type of statistic as the sole error-driving information, failing to utilize both types of complementary observations simultaneously within a unified estimation framework, thus wasting potential performance gains and robustness reserves, which is not conducive to improving estimation stability.

[0012] (3) Poor robustness to high-noise environments. Under low signal-to-noise ratio conditions, the instantaneous values ​​of correlation statistics directly calculated from sampled values ​​contain huge noise disturbances, causing severe jitter in the driving signal, which exacerbates the fluctuation of the estimated value and deteriorates the convergence accuracy. Although the difference statistics suppress some amplitude noise through the sign function, the random flipping of the sign near the zero-crossing point of the error also introduces additional disturbances. In summary, when the noise increases, the instantaneous fluctuation of a single statistic will be amplified, which can easily lead to increased jitter in the estimated value or a rapid decrease in the resolution, thereby deteriorating the accuracy of the time series deviation estimation. Existing single-statistic methods lack a dynamic adjustment mechanism for the reliability of different statistical paths, and the robustness ceiling is low.

[0013] (4) Limitations of existing hybrid approaches. It is worth noting that those skilled in the art may think of simply adding the two types of statistics together or merging them with fixed weights. However, this "static hybrid" approach cannot address the dynamic problem of "structural desensitization" and cannot continuously adjust the contribution ratio of the two types of statistics based on their real-time reliability. At a certain frequency, if statistic A itself has become ineffective, simply mixing it with the effective statistic B will only dilute the effectiveness of B and cannot shield the negative impact of A. It may even introduce abnormal fluctuations caused by the desensitization of statistic A into the system, and the result may be worse than using statistic B alone.

[0014] In summary, existing technologies face a prominent contradiction: methods relying on known signals are impractical, while practical blind estimation methods are hampered by the "structural desensitization" bottleneck of a single statistic and are vulnerable to high noise, failing to achieve stable and robust timing bias estimation in wide-bandwidth, complex electromagnetic environments. Designing an estimation mechanism that can adaptively integrate complementary error information, intelligently avoid desensitization regions, and dynamically improve noise resistance has become a pressing technical challenge in this field. Summary of the Invention

[0015] This invention proposes a time series deviation estimation method based on adaptive hybrid statistics, which solves the technical problems inherent in existing time series deviation estimation methods based on a single statistic, such as structural desensitization near specific signal frequency points and poor robustness in noisy environments.

[0016] The time-series deviation estimation method based on adaptive hybrid statistics described in this invention is applied to a multi-channel sampling system containing M channels. The method includes the following steps:

[0017] Modeling steps: Obtain the output data of each channel of the multi-channel sampling system and establish an output model; the absolute timing deviation of each channel in the output model is the unknown parameter to be estimated;

[0018] Conversion steps: The estimation objective of the output model is to estimate the absolute timing deviation of each channel, which is then converted into an estimate of the relative timing deviation between adjacent channels;

[0019] Error compensation construction steps: For any pair of adjacent channels... and +1 is called the first For adjacent channels, based on their current time Relative timing deviation The estimated value Calculate to obtain the first For adjacent channels at the current time Compensation error ;

[0020] Steps for generating complementary statistics: Based on the compensation error Parallel generation of correlation statistics Sum and difference statistics ;

[0021] Statistical smoothing steps: For the correlation statistics... and the difference type statistic Smoothing is performed separately to obtain the smoothed correlation statistics. Smoothed difference statistic ;

[0022] Adaptive weight calculation steps: Based on the aforementioned correlation statistics and the difference type statistic Calculate the smoothing error energy of the correlated path. Smoothing error energy of difference path Based on the two types of smoothing error energy and Calculate the adaptive fusion weights based on their relative size. This is to characterize the relative reliability of the two types of statistical paths, namely correlation and difference, at the current moment;

[0023] Construction steps of the mixed error term: using the adaptive fusion weights The smoothed correlation statistics and the smoothed difference statistic Perform weighted fusion to construct a mixed error term The adaptive fusion weights Used to adjust the contribution ratio of the two types of statistical paths: correlation and difference.

[0024] Timing bias update step: using the aforementioned mixed error term As the update direction, it drives the relative timing deviation estimate. Perform iterative updates;

[0025] Result recovery and output steps: Based on the updated estimated relative timing deviation between adjacent channels after convergence. Recover and output the estimated absolute timing deviation values ​​for each channel. .

[0026] Furthermore, a preferred embodiment is provided, wherein in the complementary statistics generation step:

[0027] The correlation statistics: ;

[0028] The differential statistic is constructed from the sign information of the compensation error and the local slope, and is used to characterize the relationship between the direction of the compensation error and the local trend of signal change.

[0029] ,in It is a symbolic function.

[0030] Furthermore, a preferred embodiment is provided in which a first-order infinite impulse response filter is used for smoothing in the statistical smoothing step:

[0031] (8);

[0032] (9);

[0033] in, As a smoothing factor, .

[0034] Furthermore, a preferred embodiment is provided, wherein the adaptive weight calculation step includes:

[0035] Instantaneous energy calculation steps: Calculate the instantaneous average error energy:

[0036] (14);

[0037] (15);

[0038] Energy smoothing step: Smooth the instantaneous average error energy:

[0039] (16);

[0040] (17);

[0041] in, The energy smoothing factor is 0 < <1;

[0042] Weight determination steps: Calculate the adaptive fusion weights:

[0043] (18).

[0044] Furthermore, in a preferred embodiment, in the mixed error term construction step, the mixed error term... Constructed using the following formula:

[0045] .

[0046] Furthermore, a preferred embodiment is provided in which the time-series deviation update step employs a least mean square algorithm for iterative updates:

[0047] ;

[0048] in, This is the step size parameter.

[0049] Furthermore, a preferred embodiment is provided, wherein the error compensation construction step includes:

[0050] Calculate the local slope using backward difference:

[0051] ;

[0052] in, For the first Channel output;

[0053] For the first The output of channel +1 is compensated for first order:

[0054] ;

[0055] Calculate compensation error .

[0056] Furthermore, a preferred embodiment is provided, wherein the result recovery and output steps include:

[0057] The absolute timing deviation estimate of the reference channel is set to zero;

[0058] Starting from the reference channel, the converged relative timing deviation estimates are sequentially accumulated to obtain the absolute timing deviation estimates for the remaining channels.

[0059] Furthermore, a preferred embodiment is provided, wherein the multi-channel sampling system is a time-interleaved analog-to-digital converter system.

[0060] This invention also proposes a time-series bias estimation device based on adaptive hybrid statistics, applied to a multi-channel sampling system containing M channels. The device includes the following modules:

[0061] Modeling module: acquires the output data of each channel of the multi-channel sampling system and establishes an output model; the absolute timing deviation of each channel in the output model is an unknown parameter to be estimated.

[0062] Conversion module: The estimation objective of the output model is to estimate the absolute timing deviation of each channel, and to convert it into an estimate of the relative timing deviation between adjacent channels;

[0063] Error compensation construction module: This module constructs any pair of adjacent channels. and +1 is called the first For adjacent channels, based on their current time Relative timing deviation The estimated value Calculate to obtain the first For adjacent channels at the current time Compensation error ;

[0064] Complementary statistics generation module: based on the compensation error Parallel generation of correlation statistics Sum and difference statistics ;

[0065] Statistical smoothing module: for the correlation statistics and the difference type statistic Smoothing is performed separately to obtain the smoothed correlation statistics. Smoothed difference statistic ;

[0066] Adaptive weight calculation module: based on the aforementioned correlation statistics and the difference type statistic Calculate the smoothing error energy of the correlated path. Smoothing error energy of difference path Based on the two types of smoothing error energy and Calculate the adaptive fusion weights based on their relative size. This is to characterize the relative reliability of the two types of statistical paths, namely correlation and difference, at the current moment;

[0067] Hybrid error term construction module: utilizing the adaptive fusion weights The smoothed correlation statistics and the smoothed difference statistic Perform weighted fusion to construct a mixed error term The adaptive fusion weights Used to adjust the contribution ratio of the two types of statistical paths: correlation and difference.

[0068] Timing deviation update module: using the aforementioned mixed error term As the update direction, it drives the relative timing deviation estimate. Perform iterative updates;

[0069] Result recovery and output module: Based on the updated estimated relative timing deviation between adjacent channels after convergence. Recover and output the estimated absolute timing deviation values ​​for each channel. .

[0070] The present invention has the following beneficial effects:

[0071] 1. The time series deviation estimation method based on adaptive hybrid statistics described in this invention constructs correlation-type statistics and difference-type statistics with complementary sensitivity characteristics simultaneously, and dynamically calculates adaptive weights based on the instantaneous error energy of the two types of statistical paths for fusion. This can enhance the utilization of the other type of effective statistical information when the driving force of one type of statistics weakens, thereby mitigating the performance degradation problem caused by insufficient driving force of single statistical methods near specific frequency points.

[0072] 2. The time series deviation estimation method based on adaptive hybrid statistics described in this invention performs recursive smoothing on the original statistics and their error energy, and achieves adaptive fusion based on the smoothed error energy. Under low signal-to-noise ratio conditions, it can automatically suppress the instantaneous disturbances of unreliable statistical paths caused by noise, so that the estimation process always tends to rely on more reliable error information, thereby significantly improving the estimation stability, smoothness and overall robustness of the method in high-noise environments.

[0073] 3. The time series deviation estimation method based on adaptive hybrid statistics described in this invention integrates complementary statistical information into a unified hybrid error term and updates it using recursive algorithms such as LMS. This method helps to achieve online iterative estimation while maintaining a clear algorithm structure and is easy to implement on hardware platforms such as FPGA and ASIC.

[0074] 4. The timing deviation estimation method based on adaptive hybrid statistics described in this invention establishes a "recursive estimation model for inter-channel (relative) timing deviation estimation" and restores the final estimation result to the absolute deviation of each channel. It can make a complete and consistent estimation of the timing deviation in a multi-channel sampling system with any number of channels. The output deviation vector can be directly used for subsequent digital calibration or performance evaluation, realizing the closed-loop calibration function of the system.

[0075] 5. The time series deviation estimation method based on adaptive hybrid statistics described in this invention, through the complete technical chain of complementary statistical construction, adaptive fusion and recursive update, can comprehensively improve the accuracy, stability and environmental adaptability of time series deviation estimation, so that the multi-channel sampling system can maintain excellent signal sampling performance under complex working conditions of wide bandwidth and high noise.

[0076] The time-series deviation estimation method based on adaptive hybrid statistics described in this invention is applicable to occasions such as time-interleaved analog-to-digital converters, multi-channel synchronous data acquisition systems, and distributed sensor arrays that require real-time background calibration of sampling time deviations between channels. Attached Figure Description

[0077] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0078] Figure 1 This is a flowchart illustrating the overall process of a time series deviation estimation method based on adaptive hybrid statistics, as described in one embodiment of the present invention.

[0079] Figure 2 In one embodiment of the present invention, a comparison curve of the statistical sensitivity of the correlation-only method (Corr-only), the difference-only method (Abs-only), and the method of the present invention (time series deviation estimation method based on adaptive hybrid statistics, abbreviated as HCDE) at different input frequencies is shown.

[0080] Figure 3In one embodiment of the present invention, a comparison curve of the statistical fluctuation levels of the correlation-only method (Corr-only), the difference-only method (Abs-only), and the method of the present invention (time series deviation estimation method based on adaptive hybrid statistics, abbreviated as HCDE) at different input frequencies is shown; this is used to illustrate the statistical stability of the method of the present invention near the failure frequency band.

[0081] Figure 4 In one embodiment of the present invention, a comparison curve of the equivalent time series deviation estimation variance of the correlation-only method, the difference-only method, and the method of the present invention (time series deviation estimation method based on adaptive hybrid statistics, abbreviated as HCDE) under different signal-to-noise ratio conditions is presented; it is used to show the trend of the estimation variance of the method of the present invention under varying noise conditions, and at the same time to illustrate the trend of the stability improvement of the method of the present invention under low signal-to-noise ratio conditions;

[0082] Figure 5 In one embodiment of the present invention, when using an adaptive hybrid statistics-based time series deviation estimation method, the convergence curve of the estimated time series deviation values ​​of each channel during the LMS recursive update process is shown; this is used to illustrate the convergence process and final estimation results of the method of the present invention. Detailed Implementation

[0083] To make the technical solutions and advantages of the present invention clearer, the specific embodiments of the present invention will be described in further detail and completely below with reference to the accompanying drawings. The various embodiments described below are only some preferred embodiments of the present invention, and not all of them; the various embodiments described below are intended to explain the present invention and should not be construed as limiting the present invention; reasonable combinations of the technical features defined in the various embodiments of the present invention, as well as all other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort, are within the scope of protection of the present invention.

[0084] The following are some of the technical terms used in the specific implementation methods:

[0085] Timing deviation / sampling time deviation: refers to the time difference between the actual sampling time and the ideal uniform sampling time of each channel in a multi-channel sampling system. In this specification, it can be distinguished as the relative timing deviation between adjacent channels. And the absolute timing deviation of each channel relative to the reference channel. Unless otherwise specified, the final output is an estimate of the absolute timing offset of each channel relative to the reference channel. .

[0086] Statistics: These are quantities calculated from observed data to reflect information about time-series deviations. For example, correlation statistics (…). ) and difference statistic ( Correlation statistics primarily reflect the correlation between compensation error and local slope; difference statistics primarily reflect the relationship between the direction of compensation error and local slope. The difference statistics are not simply a matter of differentiating adjacent sampled values, nor are they merely an independent judgment of the error sign; rather, they are constructed jointly by the sign information of the compensation error and the local slope. This statistic does not primarily reflect the error amplitude itself, but emphasizes the consistency between the direction of the compensation error and the local trend of signal change, characterizing time-series deviation information from another statistical perspective. Compared to common simple difference or sign comparison methods, the difference statistics described in this invention directly serve the error-driven construction in the recursive update of time-series deviations.

[0087] Smoothing statistics: These are quantities obtained by recursively smoothing the original statistics (such as through first-order IIR filtering). For example, and .

[0088] Path / Statistical Path: Refers to the complete data stream that generates and processes a specific type of statistic. For example, a "correlation path" refers to generating statistics from raw data. To get The process.

[0089] Mixed error term ( ): refers to the unified error signal formed by merging two types of smoothing statistics according to weights, which is used to drive the update of time series deviations.

[0090] Weights ( ): In the mixed error term, the correlation statistic is assigned to the smoothed version. The coefficient of takes values ​​in the range [0,1]. It is assigned to the smoothed difference statistic. The coefficient is 1- .

[0091] Implementation Method 1: A time-series deviation estimation method based on adaptive hybrid statistics is provided, applied to a multi-channel sampling system containing M channels. The method includes the following steps:

[0092] Modeling steps (step S1): Obtain the output data of each channel of the multi-channel sampling system and establish an output model; the absolute time deviation of each channel in the output model is the unknown parameter to be estimated.

[0093] Specifically: Obtain the output data sequence of each channel. (i.e., the output data of each channel), and establish the output model:

[0094] ;

[0095] in, For the first The absolute timing deviation of each channel is an unknown parameter to be estimated;

[0096] Transformation step (step S2): The estimation objective of the output model is to estimate the absolute timing deviation of each channel, and to transform it into an estimate of the relative timing deviation between adjacent channels;

[0097] Specifically: the conversion step, or parameter definition step, defines the first... The first channel and the first The relative timing deviation between +1 channels is:

[0098] ,in = 0, 1, …, -2;

[0099] At this point, the output model of the multi-channel sampling system is a recursive estimation model for inter-channel (relative) timing deviation estimation;

[0100] Error compensation construction steps (step S3): For any pair of adjacent channels... and +1 is called the first For adjacent channels, based on their current time Relative timing deviation The estimated value Calculate to obtain the first For adjacent channels at the current time Compensation error Note that this step also constructs the local slope. ;

[0101] Complementary statistic generation step (step S4): Based on the compensation error (and local slope) Parallel generation of correlation statistics Sum and difference statistics ;

[0102] Statistical smoothing step (step S5): For the correlation statistics and the difference type statistic Smoothing is performed separately to obtain the smoothed correlation statistics. Smoothed difference statistic ;

[0103] Adaptive weight calculation step (step S6): Based on the correlation statistic and the difference type statistic Calculate the smoothing error energy of the correlated path. Smoothing error energy of difference path Based on the two types of smoothing error energy and Calculate the adaptive fusion weights based on their relative size. This is to characterize the relative reliability of the two types of statistical paths, namely correlation and difference, at the current moment;

[0104] Construction step of the mixed error term (step S7): using the adaptive fusion weights The smoothed correlation statistics and the smoothed difference statistic Perform weighted fusion to construct a mixed error term The adaptive fusion weights It is used to adjust the contribution ratio of the two types of statistical paths, namely correlation and difference, rather than to adjust the update step size of a single path;

[0105] Timing deviation update step (step S8): using the aforementioned mixed error term As the update direction, it drives the relative timing deviation estimate. Perform iterative updates;

[0106] Result recovery and output step (step S9): Based on the updated estimated relative timing deviation between adjacent channels after convergence. Recover and output the estimated absolute timing deviation values ​​for each channel. .

[0107] The result recovery and output steps include:

[0108] The absolute timing deviation estimate of the reference channel is set to zero;

[0109] Starting from the reference channel, the converged relative timing deviation estimates are sequentially accumulated to obtain the absolute timing deviation estimates for the remaining channels.

[0110] For example, taking channel 0 as the reference channel, let its absolute timing deviation estimate be... = 0;

[0111] for = 1, 2, ..., -1, calculated through accumulation:

[0112] ;

[0113] in, For the convergence of the first Estimates of the relative timing deviation between adjacent channels.

[0114] This embodiment provides a timing bias estimation method based on adaptive hybrid statistics, applied to a multi-channel sampling system with M channels (e.g., a time-interleaved analog-to-digital converter, TI-ADC). The method aims to estimate and output the timing bias estimate of each channel relative to a reference channel. Its core lies in constructing two error statistics with complementary characteristics and adaptively fusing them based on the relative reliability characterized by the recent error energy of the two statistical paths. This generates a unified hybrid error term to drive adaptive iterative updates, thereby overcoming the performance degradation problem of single-type statistics under specific signal conditions and achieving highly robust timing bias estimation.

[0115] In this embodiment, the time series deviation estimation method based on adaptive hybrid statistics has the following advantages:

[0116] (1) It can simultaneously utilize two types of complementary statistical information to improve the stability of the estimation:

[0117] Simultaneously, correlation-type statistics and difference-type statistics are constructed and fused together at the error layer. Since the two types of statistics have different sensitivities to time series deviations, they can complement each other to provide estimation information under different working conditions, thus avoiding the problem of insufficient information utilization by single statistical methods.

[0118] (2) It can mitigate the desensitization problem of a single statistic near a specific frequency point:

[0119] Correlation statistics may exhibit decreased sensitivity under certain frequency conditions, while difference statistics can provide supplementary driving force under other conditions. By combining the two types of statistics into a unified estimation index through mixed statistics, the failure of a single path near a specific frequency point can be mitigated.

[0120] (3) It has better noise robustness:

[0121] Both types of statistics and their error energy are smoothed, and adaptive fusion is then implemented on this basis. This method can reduce the disturbance of noise to instantaneous statistics, so that the estimation results maintain good smoothness and stability under different SNR conditions.

[0122] (4) The logic is clear and easy to implement recursively:

[0123] The process follows the steps of “establishing a sampling model – constructing errors – generating two types of statistics – smoothing – fusing and constructing mixed errors – recursively updating – restoring multi-channel time series bias”. The steps are clearly defined and suitable for iterative estimation in multi-channel sampling systems.

[0124] (5) It can achieve stable estimation of timing deviations in multiple channels:

[0125] By recursively updating the timing deviation of adjacent channels, stable multi-channel timing deviation estimation results can be obtained, which are applicable to multi-channel synchronous sampling and time-interleaved sampling systems.

[0126] Implementation Method 2: In the time series deviation estimation method based on adaptive mixed statistics, the modeling step (step S1):

[0127] This step aims to establish an accurate mathematical model for the entire estimation method. This model uses mathematical formulas to describe the actual output signal of each (sampling) channel in the multi-channel sampling system, explicitly including the unknown parameter to be estimated—timing deviation. Establishing this model is fundamental to all subsequent derivations and algorithm design.

[0128] Acquiring output data from a multi-channel sampling system: This refers to collecting the sequence of digital signals output by each sampling channel of the multi-channel sampling system at multiple sampling times from actual hardware (such as a time-interleaved ADC chip) or a simulation environment. These data serve as the input and basis for all subsequent calculations.

[0129] Specifically:

[0130] Assume a multi-channel sampling system includes The sampling channel, the first The output (data) of each (sampled) channel is represented as follows:

[0131] (1);

[0132] This formula gives the output model of a multi-channel sampling system;

[0133] Symbol meaning:

[0134] The total number of sampling channels in a multi-channel sampling system;

[0135] (Sampling) Channel Index = 0, 1, ..., -1;

[0136] : Sampling time index, representing the first sampling time. The system sampling period, or the first system sampling period Time, Number The next iteration;

[0137] The first multi-channel sampling system The first channel in the The output (data), or output data sequence, at each sampling time of a system cycle;

[0138] The original continuous-time analog signal being sampled (or to be sampled);

[0139] The average sampling period of a multi-channel sampling system; if the sampling rate of a single channel is... ,but The entire system operates in a periodic manner. Work, each channel is delayed sequentially. sampling;

[0140] : No. The absolute timing deviation of each channel, that is, the actual sampling time of the channel relative to its ideal sampling time. The deviation of ) is one of the unknown parameters that needs to be estimated;

[0141] Noise term, number The first channel in the Additive noise at any given moment.

[0142] Since each channel samples the same signal They are only staggered in time, so their output data should ideally satisfy a defined time alignment relationship. Timing deviations disrupt this relationship.

[0143] Therefore, the goal of this method (timing deviation estimation) is to analyze the output data of each sampling channel. The timing inconsistency between channels is estimated in reverse to determine the timing deviation between channels that causes this inconsistency.

[0144] Implementation Method 3: In the time series deviation estimation method based on adaptive hybrid statistics, the transformation step (or parameter definition step, i.e., step S2):

[0145] This step redefines and models the unknown parameters that need to be estimated. Instead of directly estimating the absolute deviation of each channel, it transforms it into estimating the relative deviation between adjacent channels to simplify the estimation model and utilize the local relationships between channels.

[0146] Specifically:

[0147] The temporal relationship between channels is expressed as the (relative) temporal deviation between adjacent channels, and a recursive estimation model is established based on this:

[0148] (2);

[0149] Symbol meaning:

[0150] : No. +1 channel relative to the first Timing skew of each channel. If all channels are perfectly aligned, then all = 0;

[0151] : respectively the first and the +1 channel absolute timing deviation.

[0152] Significance and Function: This formula defines the relative timing deviation between adjacent channels. Through this definition, the absolute deviations of all channels are expressed as { The estimation problem of} is transformed into the estimation of} -1 relative deviation { The estimation problem of}. As long as all are estimated... and in a channel (such as Using 0 as a reference, the absolute (timing) deviation of all channels can be recovered by accumulation (recursion).

[0153] In the above manner, the (absolute) timing deviation estimation process can be described as a recursive (relative timing) estimation process between adjacent channels: because It only involves two adjacent channels. and +1, thus bias estimation can be performed independently, in parallel, or sequentially for each pair of adjacent channels; this "recursion" refers to indexing along the channels. Process them one by one (or one pair at a time), rather than recursively over time; this simplifies estimation and reduces problem complexity.

[0154] Implementation Method 4: In the time series deviation estimation method based on adaptive hybrid statistics, the error compensation construction step (step S3) is as follows:

[0155] Constructing first-order compensation errors for adjacent channels: This step is one of the core components of the estimation. The aim is to utilize the current time (the...) (moment) The estimated value The prediction determines the relationship that the data from two adjacent channels should satisfy if this estimate is correct, and compares it with the actual data to generate a residual signal, which compensates for the error. This error will serve as a source of information driving the update of the estimate.

[0156] For any pair of adjacent channels ( , +1), based on the current (relative) time series deviation estimate Construct a first-order time compensation process: that is, for any pair of adjacent channels ( , +1), utilizing the current iteration (e.g., the 1st iteration) The iteration, or the th iteration The estimated (relative) time series deviation obtained at time (time) The data in one channel is compensated for a time offset to align with the time point of the other channel.

[0157] First, a local slope is constructed using the difference between adjacent sampling points (the local slope is used to characterize the rate and direction of signal change with time near the current sampling point) to approximate the slope:

[0158] (3);

[0159] This formula is used to approximate the instantaneous rate of change (derivative) of a signal near a certain sampling point; the... Obtained using backward difference calculation;

[0160] Symbol meaning:

[0161] : No. The first channel in (the first) Approximate local slope of the output signal (per system cycle);

[0162] : No. Each channel is currently ( ) and the previous system cycle ( -1) of the sampled output.

[0163] Under the first-order approximation, the signal has a small time shift. The change within can be expressed as Here, backward difference is used to approximate the differential, which is simple to calculate.

[0164] Then, using the local slope and the current (relative) time series deviation estimate, the first... The output of each channel is compensated for in the first order (time):

[0165] (4);

[0166] This formula utilizes a first-order Taylor expansion. Perform time offset compensation;

[0167] Symbol meaning:

[0168] : Regarding the first Channel output The value obtained after first-order compensation; the purpose is to align it in time to the [previous / next] order. Ideal sampling time for the channel nearby;

[0169] : No. The raw output of the channel;

[0170] : Current time (n) pair The estimated value;

[0171] : No. Local slope (approximate value) of the channel;

[0172] Formula meaning: If If it is completely accurate and the first-order approximation holds true, then the compensated... It should be very close to Compensation amount This represents the difference in signal values ​​between channels predicted based on the current (relative) deviation estimate and the rate of change of the signal (local slope).

[0173] Further define the compensation error:

[0174] (5);

[0175] This formula is used to calculate the residual after compensation;

[0176] Symbol meaning:

[0177] The inconsistency error remaining after compensation of adjacent channels under the current (relative) deviation estimate, i.e., the compensation error, or the error remaining after first-order compensation, is the error in the second-order channel. Channel data and the first The difference between channel data; it includes an estimate of the current timing bias. Compared with the true value Information on the differences between them;

[0178] Formula meaning: This forms the basis for all subsequent statistics. Ideally, when the time-series bias is fully compensated, It should approach zero-mean noise. If there is an error, then It will contain information related to this error, which can then be used to update the time series bias estimate. .

[0179] Implementation Method 5: In the time series deviation estimation method based on adaptive hybrid statistics, the complementary statistics generation step (step S4) includes the following steps for constructing correlation statistics:

[0180] Construct complementary error statistics: based on the compensation error and local slope Two types of error-driving signals with different statistical properties are constructed in parallel. This step involves compensating for the error. The first type of error information (error-driven signal) is extracted; its principle is based on the "correlation between error and signal change trend".

[0181] Based on the compensation error obtained in step S3 With local slope Construct correlation statistics:

[0182] (6);

[0183] This formula defines a correlation statistic; it is essentially an error compensation measure. With local slope Instantaneous multiplication (which can be regarded as a kind of instantaneous correlation operation);

[0184] Symbol meaning:

[0185] : No. For adjacent channels in the first Correlation statistics at different times.

[0186] Formula meaning: The magnitude and sign of the error reflect the direction and magnitude of the timing bias estimation error. When the bias estimation is insufficient or excessive, and It will present a specific positive and negative relationship, thus It will deviate from zero, and its expected value is a function of the time series bias estimation error, which can be used as the gradient direction to drive the update of the estimate.

[0187] The correlation statistic, through instantaneous multiplication, reflects the consistency (correlation) between the compensation error and the local trend of change. Its expected value is proportional to the time series deviation estimation error: when the signal is changing ( When the value is not zero, if there is uncompensated timing deviation, a related compensation error will be generated. ; Link these two together and quantify the consistency between them.

[0188] If the current time series bias estimate deviates from the true value, the correlation statistics will show corresponding changes, thus providing driving information for subsequent updates: Used as an "error-driven signal"; within the adaptive filtering framework, The expected value can be regarded as the gradient of the cost function with respect to the time series bias estimate (or proportional to it), and therefore can be used to guide the estimate to converge to the true value.

[0189] Implementation Method 6: In the time series bias estimation method based on adaptive mixed statistics, the complementary statistics generation step (step S4) includes the following steps for constructing the difference-type statistics:

[0190] This step involves compensating for errors. The second type of error information, which has complementary characteristics, is extracted from it. Its principle focuses more on the sign (direction) information of the error.

[0191] Based on the compensation error obtained in step S3 Based on its symbolic information, construct the difference type statistic:

[0192] (7);

[0193] This formula defines the difference statistic; it takes the compensated error. The sign, and then the local slope Multiply;

[0194] Symbol meaning:

[0195] : No. For adjacent channels in the first Difference statistics at time points;

[0196] : Sign function, output +1 when the input is positive, output -1 when the input is negative, and output 0 when the input is zero.

[0197] Formula meaning: right The magnitude of the error is insensitive; only its sign matters. This makes it insensitive to the "overshoot" of large-amplitude errors, and in... When the value is very small, as long as the sign is determined, it can still provide a clear driving direction. In some cases (such as at a specific frequency point), its statistical characteristics are similar to... Complementary.

[0198] The difference statistics are used to emphasize the relationship between the direction of the compensation error and the local slope. Compared with correlation statistics, they are more sensitive to larger deviations and sign changes, and can complement correlation statistics. Unlike processing that only subtracts adjacent sample values ​​or only extracts the error sign, the difference statistics in this embodiment are based on the joint construction of compensation error and local slope.

[0199] The phrase "emphasizing the direction of error (information)" refers to the fact that the core of the difference statistic is... The symbol. In certain scenarios (e.g., when...) When the amplitude is small but the direction is clear, or when the driving force of correlation statistics weakens but the error direction can still be stably determined, difference statistics It can still provide more More reliable driving information, thus complementing the functions of correlation statistics.

[0200] In summary, the differential statistics in this embodiment differ from processing methods that only utilize the difference, absolute difference, or sign comparison between consecutive sampling points. Its core lies in combining the directional information of the compensation error with the signal change trend represented by the local slope to construct an error-driving signal for time-series bias estimation. Through this construction, the differential statistics can still maintain an effective indication of the update direction even in scenarios where the driving force of certain correlation statistics weakens but the error direction can still be stably determined, thus complementing the correlation statistics.

[0201] Implementation Method 7: In the time series deviation estimation method based on adaptive mixed statistics, the statistical smoothing step (step S5) is as follows:

[0202] Due to noise and signal fluctuations, the directly calculated and The instantaneous values ​​fluctuate greatly (large variance). This step uses low-pass filtering (smoothing) to extract the trend of its statistical expectation, thereby improving stability.

[0203] Due to limited observation length and noise, correlation and difference statistics may exhibit transient fluctuations. To suppress the effects of noise and transient fluctuations and improve statistical stability, recursive smoothing is performed on both types of (original) statistics.

[0204] The preferred method is first-order IIR smoothing, which yields the smoothed statistics:

[0205] (8);

[0206] (9);

[0207] This is a first-order infinite impulse response (IIR) smoothing filter, also known as an exponentially weighted moving average;

[0208] Symbol meaning:

[0209] , The smoothed correlation and difference statistics are used for subsequent fusion.

[0210] Smoothing factor ; The closer it is to 1, the stronger the smoothing effect, but the slower the response to new data.

[0211] Formula meaning: Through recursive smoothing, it effectively suppresses... and By eliminating high-frequency noise and transient disturbances, a smoother sequence that better reflects its statistical expectation was obtained. and This provides a more stable input for subsequent integration.

[0212] After smoothing, we obtain correlation-type smoothing statistics and difference-type smoothing statistics for subsequent fusion, which provide higher-quality, less volatile input signals for subsequent fusion operations. and .

[0213] Implementation Method 8: In the time series deviation estimation method based on adaptive hybrid statistics, the adaptive weight calculation step (step S6) is as follows:

[0214] Adaptive weight calculation based on error energy: This step is an improvement on existing technologies. It dynamically assesses the relative reliability of the two statistical paths based on the relative magnitude of their recent error energies, and calculates the adaptive fusion weights accordingly. The core idea is to allocate weights based on the relative reliability of the two types of statistical paths. These weights are used to adjust the contribution ratio of the two types of statistical paths to the mixed error term, rather than adjusting the LMS step size of a single path.

[0215] To mitigate the failure of a single statistic at specific frequencies or under specific noise conditions, an error energy-driven adaptive weighting strategy is adopted: Because and Reliability varies under different signal conditions (e.g., at certain frequency points). The expected value is very small, and it loses its driving force. Fixed weights cannot cope with all scenarios; adaptive weights aim to make the estimation process continuously biased towards the more reliable statistics at present, so as to achieve soft decision fusion of the two types of statistical information.

[0216] The applicant further recognized that simply introducing two types of statistics cannot automatically achieve a stable fusion effect. The key lies in how to dynamically adjust the contribution ratio of the two statistical paths based on their differences in effectiveness at the current moment. Therefore, this implementation uses smoothed error energy as a representation of path reliability. This is because the instantaneous value of a single statistic is easily affected by noise and random disturbances, making it difficult to stably reflect the path state; while the smoothed error energy can characterize the recent fluctuation level and stability of each statistical path with lower implementation complexity. Based on this, normalizing the two types of smoothed error energy yields continuously varying and bounded fusion weights, enabling soft-decision allocation of the mixed error term between the two types of statistical paths. This design differs from the fixed-weight approach, which cannot adjust with changing operating conditions, and also from the hard-switching approach, which easily introduces abrupt changes when the reliability of the two paths is close.

[0217] First, calculate the correlation path and the difference path separately (in Instantaneous average error energy at time:

[0218] (14);

[0219] (15);

[0220] This formula calculates all channel pairs ( The original statistics of -1 pairs are in The average of the instantaneous squared values ​​at time t is used as an approximation of the "error energy" of the path at that time t.

[0221] Symbol meaning:

[0222] , : Instantaneous average error energy for time-dependent paths and differential paths.

[0223] Formula meaning: and This reflects the "intensity" or "activity" of the statistics for each path at that moment. Ideally, when the statistics for a certain path can provide effective driving information, its expected value should be relatively large (but note that high "energy" does not directly equate to high "reliability"; it needs to be understood in conjunction with subsequent smoothing and normalization logic). Averaging across all channel pairs is to comprehensively utilize system information and improve the stability of the estimation.

[0224] Then, the (instantaneous) error energy is recursively smoothed to obtain a stable energy estimate:

[0225] (16);

[0226] (17);

[0227] Similarly, first-order IIR smoothing is used to adjust the instantaneous error energy. and Perform low-pass filtering;

[0228] Symbol meaning:

[0229] , Error energy of smoothed correlated and differential paths;

[0230] Energy smoothing factor, 0 < <1; usually Take a larger value (such as close to 1) to obtain a smooth energy estimate.

[0231] Formula meaning: Smoothed error energy and It reflects the average level of the recent "energy" of each statistical path, and is more stable and representative of its statistical characteristics than the instantaneous value.

[0232] Finally, the adaptive weights are determined based on the normalization relation:

[0233] (18);

[0234] (19);

[0235] This formula defines the adaptive weights. The specific calculation method; it is essentially the proportion of the smoothing error energy of another path to the sum of the total energy; this design makes the weights It automatically favors statistical paths with smaller current error energy and relatively more stable fluctuations; compared with fixed weights or hard switching, it helps to reduce abrupt changes caused by path switching.

[0236] Symbol meaning:

[0237] :exist Time intervals are assigned to smoothed correlation statistics. The weights are assigned accordingly; the weights assigned to the smoothed difference statistic are 1- .

[0238] Formula meaning: This is one of the improvements over existing technologies. Its design logic is: the smaller the error energy of a certain path, the closer its statistics are to its expected value (i.e., less noise or more stability), or the clearer its driving direction, thus it is considered more "reliable" and should be given higher weight in the mixing process. For example, if... very small and Very large, then = / (small + large) ≈ 1, weight bias Through this normalization, the weights It is automatically constrained to the [0,1] interval and achieves dynamic measurement of reliability.

[0239] When the error energy of a correlated path is small and its reliability is high, The corresponding weights increase accordingly; when the differential path is more reliable, the relevant weights decrease accordingly; that is, the direction of the adaptive adjustment of weights is: the weights tilt towards the statistical path that is more reliable in an instant.

[0240] This method allows the estimation process to automatically skew towards a more reliable statistical path; that is, through the aforementioned weighting calculation based on error energy, the mixed error term... It can adaptively select the most reliable error information, thereby improving the overall stability and robustness of the estimator.

[0241] Implementation Method 9: In the time series deviation estimation method based on adaptive mixed statistics, the mixed error term construction step (step S7) is as follows:

[0242] Constructing a hybrid error term and cost function: The smoothed two types of statistics are merged into a unified error driving signal so as to comprehensively utilize the two types of complementary statistical information under the same recursive update framework.

[0243] To utilize the complementary properties of the two types of statistics, the smoothed correlation and difference statistics are fused to construct a unified mixed error term:

[0244] (10);

[0245] This formula defines the mixed error term. It is a weighted combination of two types of smoothing statistics, which integrates the complementary information of correlation statistics and difference statistics, and can automatically adjust the fusion ratio according to their reliability;

[0246] Symbol meaning:

[0247] : The mixed error term used to ultimately drive timing bias updates;

[0248] Assigned to The adaptive weights, or the weights of related paths;

[0249] (1- ): Naturally, it is allocated to The weight.

[0250] Formula meaning: Through weighted fusion, It also includes from and Error information. Ideally, It can dynamically adjust based on the current reliability of both, so that It is always dominated by more reliable information, thus achieving better and more stable performance than a single statistic.

[0251] Among them, the weights of related paths ,satisfy:

[0252] (11);

[0253] This inequality constrains the weights. The range of values ​​is used to ensure that the mixing is a reasonable interpolation between the two, rather than an amplification.

[0254] Furthermore, the corresponding cost function can be constructed:

[0255] (12);

[0256] This formula defines the instantaneous cost function;

[0257] Symbol meaning:

[0258] : No. For the channel in the The (instantaneous) cost function at time 1.

[0259] Formula meaning: Within the Least Mean Square (LMS) adaptive algorithm framework, the objective is typically to minimize the mean square value of the error signal. Here, we will... If considered as "error", then It is in its second norm form. Minimize The expectation, i.e., the driving force The time series bias estimate tends to zero, thus indirectly causing the time series bias estimate to converge to the true value. This provides a theoretical basis for the subsequent LMS update formula.

[0260] The mixed error term serves as a unified estimation index for subsequent time series bias updates: It is the final output of the entire estimator front-end (signal processing and fusion part), which will be used as the core feedback signal input to the parameter update part of the back-end.

[0261] Therefore, the mixed error term does not mechanically superimpose the two types of statistics. Instead, within a unified recursive update framework, its contribution ratio is continuously adjusted based on the relative reliability of the two statistical paths, ensuring that the more stable and effective statistical information dominates the update process. This mechanism retains the complementary advantages of correlation and difference statistics while avoiding the problems of fixed-ratio mixing failing to adapt to changes in operating conditions and the discontinuities easily generated by hard switching. Therefore, when the adaptive fusion mechanism is combined with the LMS update step, the weights serve to adjust the composition of the mixed error term, rather than replacing or altering the step size adjustment mechanism of the LMS algorithm itself.

[0262] Implementation Method 10: In the time series deviation estimation method based on adaptive hybrid statistics, the time series deviation update step (step S8) is as follows:

[0263] LMS-based timing skew (recursive) update: This step utilizes the previously obtained mixed error term. The least mean square (LMS) adaptive algorithm is used to iteratively update the time series deviation estimate.

[0264] Within the recursive update framework, the time series bias estimate is iteratively updated based on the mixed error term, preferably using the LMS (algorithm update formula) form:

[0265] (13);

[0266] Symbol meaning:

[0267] : No. The iteration (or the) (moment) The estimated value.

[0268] The step size parameter is a small positive number that controls the update step size and is used to balance the convergence speed and steady-state error.

[0269] : Mixed error term, used as update driving signal.

[0270] Formula meaning: This formula achieves adaptive iteration of the time series bias estimate. The update direction is given by the mixed error term, meaning it moves towards making the mixed error term... The reduced direction adjustment estimate; where the mixed error term is formed by weighting two types of statistical paths, rather than by changing the LMS step size. When When it approaches 0, the estimated value It tends to stabilize and, theoretically, will converge to the true value. nearby.

[0271] After updating the (relative) timing biases of all adjacent channels, the (absolute) timing bias estimation results of each channel relative to the reference channel can be recovered through a linear accumulation relationship. This involves understanding how to extract the estimated relative biases from the timeline. To obtain the final required absolute deviation :

[0272] Typically, the deviation of the reference channel (e.g., channel 0) is set to 0, i.e. = 0, then accumulate:

[0273] because = 0, = + ,so = ;

[0274] because = , = + ,so = + ;

[0275] because = + , = + ,so = + + ;

[0276] And so on:

[0277] for = 1, 2, ..., -1, calculated through accumulation:

[0278] ;

[0279] in, For the convergence of the first Estimates of the relative timing deviation between adjacent channels.

[0280] Implementation Method 11: In the time series deviation estimation method based on adaptive hybrid statistics, the result recovery and output step (step S9):

[0281] Output (final) timing deviation estimation results: The obtained timing deviation estimates of adjacent channels are accumulated and recovered to obtain the timing deviation estimation results of each channel relative to the reference channel, and the final timing deviation estimation vector is output for subsequent timing compensation, background calibration or performance analysis.

[0282] Repeat the steps "Constructing first-order compensation error" to "LMS-based time-series bias recursive update" iteratively until the estimated value converges.

[0283] Finally, the converged relative timing deviation estimates of adjacent channels are... Perform linear accumulation, and using any channel (e.g., channel 0) as a reference (assuming its deviation is 0), recover and output the absolute timing deviation estimate vector of all channels relative to the reference channel:

[0284] (generally =0).

[0285] The output is an estimated value in the form of a time difference; when a normalized representation is required, it can be converted according to the sampling period. This result (vector) can be directly used for subsequent real-time (online) digital calibration of the system (such as interpolation compensation of sampled data), or used in the background to evaluate system performance (such as offline performance analysis), adjust hardware parameters, etc.

[0286] By constructing complementary statistics and a reliability-based adaptive fusion mechanism, the performance degradation problem that may occur in single-type error statistics at specific frequency points or in noisy environments is effectively overcome, and the robustness, stability and convergence performance of timing bias estimation of multi-channel sampling systems are significantly improved.

[0287] It should be noted that existing technologies in this field may disclose schemes for estimating time-series bias in multi-channel sampling systems using correlation statistics combined with LMS recursive updates. These schemes disclose a basic calibration framework of "constructing correlation statistics - adaptive update." However, even within this framework, existing technologies have not disclosed or taught the following core concept: simultaneously constructing two types of statistics—correlation and difference—that are complementary in their sensitivity characteristics, and further adaptively determining the fusion weights based on an assessment of the real-time reliability of the two statistical paths (such as their smoothing error energy), thereby generating a hybrid error-driven signal. This invention achieves a significant performance leap based on this concept not disclosed in existing technologies.

[0288] It should be noted that in existing technologies, only one type of statistic, either correlational or difference-based, is typically selected as the sole error-driving information. This fails to utilize two complementary types of observations simultaneously within a unified estimation framework, resulting in the loss of potential performance gains and robustness reserves, which is detrimental to improving estimation stability.

[0289] The applicant further recognized that correlation statistics and difference statistics are not simply two interchangeable observables, but rather two types of statistical paths with different failure mechanisms in the problem of time series bias estimation. Correlation statistics primarily rely on the correlation between compensation error and local slope; when this correlation weakens under certain input conditions, its driving force on time series bias decreases significantly. Difference statistics, on the other hand, emphasize the consistency between the direction of compensation error and the local trend of signal change. Even when the driving force of correlation statistics weakens but the directional information can still be stably discerned, it can still provide an effective update direction. Conversely, when difference statistics fluctuate more due to sign flipping, correlation statistics can provide smoother driving information. Therefore, the two types of statistics are statistically complementary. Simply introducing both types of statistics is insufficient to automatically solve the problem of a single statistic failing; it is also necessary to dynamically adjust the contribution ratio of the two statistical paths based on their differences in effectiveness under current conditions.

[0290] In existing technologies, there has long been a technical inertia or bias in the field: when designing blind estimation schemes, only one type of statistic, either correlational or difference-based, is typically selected as the sole error-driving information. The underlying belief is that both can serve as error drivers and are mutually substitutable parallel technical choices. This underlying belief results in existing technologies failing to utilize two complementary types of observations simultaneously within a unified estimation framework, thus losing potential performance gains and robustness reserves, and hindering the improvement of estimation stability.

[0291] However, after in-depth research, the applicant realized that correlation statistics and difference statistics are not simply two interchangeable observables, but rather two statistical paths with different and complementary failure mechanisms in the problem of time series bias estimation.

[0292] Correlation statistics rely on the amplitude correlation between the error and the signal slope, and become insensitive under weak correlation conditions; while difference statistics rely on the consistency between the error sign and the slope direction, and are insensitive to amplitude changes. More importantly, the "failure points" (i.e., operating conditions where sensitivity drops sharply) of the two types of statistics usually do not coincide in the frequency domain and other areas. Therefore, schemes that only introduce one type of statistic have inherent "structural blind spots" in their performance that cannot be eliminated through self-optimization.

[0293] The contribution of this invention lies in its breakthrough from the conventional thinking of "choosing one over the other," recognizing that it is essential to simultaneously utilize and effectively integrate these two types of complementary information in order to construct an estimator that is robust across all operating conditions. This constitutes a novel approach to solving the long-standing technical challenge of "structural desensitization."

[0294] It should be noted that even if it is recognized that two types of statistics need to be used, how to effectively integrate the two rather than simply superimpose them is the next specific technical problem that this invention needs to solve.

[0295] Simple fixed-ratio mixing cannot dynamically respond to changes in operating conditions; hard switching based on a fixed threshold will introduce discontinuous disturbances caused by sudden path changes.

[0296] To address this, the present invention proposes an adaptive fusion weight. This adaptive fusion weight is not used to adjust the step size of the single-path update formula, but rather to allocate the contribution ratio of the correlation-type statistical path and the difference-type statistical path to the mixed error term.

[0297] The design of the weights is based on the fact that the stability and effectiveness of the two types of statistical paths are not the same under different input frequencies, noise levels and deviation conditions. Therefore, a quantity that can reflect the recent reliability of the path is needed to achieve continuous fusion.

[0298] Specifically, using smoothing error energy as a characterization of path reliability has the engineering implication that a smaller error energy for a path generally indicates less recent fluctuation and more stable statistical output, thus allowing for higher weighting during fusion. By normalizing the two types of smoothing error energy, the weights can be continuously varied within a bounded range, thereby achieving soft-decision fusion between the two types of statistics.

[0299] Compared with the fixed-ratio mixing method, this mechanism can dynamically adjust the fusion ratio according to changes in operating conditions; compared with the hard switching method, this mechanism is beneficial to reducing discontinuous disturbances caused by sudden path changes.

[0300] Implementation Method 12: The present invention will be further described in detail below with reference to specific embodiments. The following embodiments are for illustrative purposes only and should not be considered as limitations on the present invention.

[0301] Example 1: Performance verification under single-frequency sweep condition:

[0302] This embodiment is used to verify the differences in statistical characteristics of the method of the present invention at different input frequencies, especially to analyze the sensitivity and statistical fluctuation changes near the structural desensitization frequency band.

[0303] A simulation model of a 4-channel time-interleaved sampling system was established with a sampling rate of 1 GHz. Each channel was preset with a random, unknown timing bias. For comprehensive testing, nine equally spaced frequency points within the range of 50 MHz to 450 MHz were selected as the frequencies of the input sinusoidal signal.

[0304] The implementation steps are as follows (the method of this invention, abbreviated as HCDE):

[0305] Step 1: Collect output data from each channel and establish a timing deviation model.

[0306] Step 2: For each pair of adjacent channels, construct a first-order compensation error and generate correlation statistics accordingly. Sum and difference statistics .

[0307] Step 3: Perform first-order IIR smoothing on both types of statistics.

[0308] Step 4: Calculate the smoothed error energy of the two types of statistical paths, and obtain the adaptive fusion weights accordingly. Thus, a mixed error term is constructed. .

[0309] Step 5: Through analysis The statistical characteristics at different input frequencies are used to evaluate the sensitivity and stability of the method and to provide a basis for the construction of subsequent fusion error terms.

[0310] In contrast, two single-statistic methods were implemented simultaneously: the "Corr-only" method, which uses only correlation statistics, and the "Abs-only" method, which uses only difference statistics.

[0311] The results are as follows Figure 2 and Figure 3 As shown:

[0312] Figure 2 The sensitivity curves show that the "Corr-only" method is effective at certain frequency points (e.g., A significant decrease in sensitivity occurs near the [frequency band], while the method of the present invention (HCDE) exhibits a relatively smooth sensitivity change trend throughout the entire frequency band.

[0313] Figure 3 The statistical fluctuation curves further demonstrate that, near the frequency band where the "Corr-only" method fails, the statistical fluctuations of the method of this invention are relatively smooth, showing good statistical stability.

[0314] The above results show that correlation statistics and difference statistics have different statistical response characteristics under different input frequency conditions, while the method of this invention exhibits more balanced statistical characteristics in the frequency dimension. This provides experimental basis for the subsequent construction of the fusion error term.

[0315] Depend on Figure 2 and Figure 3 It is evident that the correlation statistics exhibit a structural performance degradation around the normalized frequency of approximately 0.25. This frequency band can be considered a representative desensitization band, and further comparisons can be made of the estimation performance of different methods at this frequency point.

[0316] Accordingly, a normalized frequency is selected within the representative desensitization frequency band. As a local comparison frequency point, in order to reduce the impact of single random noise on the results, 10 repeated simulations were performed at this frequency point, and the average root mean square error and the average maximum absolute error were used as evaluation indicators to compare the correlation-only method, the difference-only method, the fixed weight hybrid method, and the method of this invention. The results are shown in Table 1.

[0317] Table 1. Performance comparison of different methods at representative desensitization frequencies.

[0318] Only correlation method 6.1974 9.4670 Difference-only fractal method 6.3481 9.6719 Fixed-weight hybrid method (0.2) 6.4099 9.6749 Method of the present invention 6.1625 9.4103

[0319] As can be seen from Table 1, in the normalized frequency At representative desensitization frequencies, the mean root mean square error and mean maximum absolute error of the method of this invention are both smaller than those of the correlation-only method, the difference-only method, and the fixed-weight hybrid method. This result indicates that near frequencies where a single statistic exhibits structural performance degradation, the method of this invention, through adaptive fusion of correlation-type and difference-type statistics, can achieve better estimation accuracy.

[0320] The above results show that correlation statistics and difference statistics have different statistical response characteristics under different input frequency conditions. At the representative structurally desensitized frequency point, the method of the present invention is superior to the comparison method in terms of estimation accuracy, thus demonstrating that the adaptive hybrid statistical mechanism can effectively improve the estimation performance of the single statistical method in this type of frequency band.

[0321] Example 2: Robustness verification under different noise conditions:

[0322] This embodiment is used to verify the estimation variance variation trend of different statistical methods in a high-noise environment, and to analyze the stability performance of the method of the present invention under low signal-to-noise ratio conditions.

[0323] Based on Example 1, the normalized input frequency is fixed at 0.3. The power of the additive white Gaussian noise is varied to gradually reduce the signal-to-noise ratio (SNR) of the input signal from 50 dB to 10 dB. For each SNR setting, the "Corr-only" method, the "Abs-only" method, and the method of this invention are run respectively, and the equivalent time-series bias variance of the final estimation result of each method is calculated. This variance directly reflects the estimation accuracy.

[0324] Implementation results are as follows Figure 4 As shown:

[0325] As the SNR decreases, the estimated variance of the equivalent time series bias using both single-statistic methods shows an increasing trend. In contrast, the method of this invention exhibits a lower estimated variance and a more gradual trend across the entire SNR variation range.

[0326] This indicates that the method of the present invention is beneficial for improving the stability of time series bias estimation under low signal-to-noise ratio conditions and for mitigating the tendency of estimation variance to deteriorate with increasing noise.

[0327] The above results further illustrate that the combination of correlation statistics and difference statistics in this invention not only helps to alleviate the limitations of a single statistic under specific frequency conditions, but also helps to maintain a relatively stable error driving capability under low signal-to-noise ratio conditions, thus demonstrating the rationality of the fusion mechanism in the noise dimension.

[0328] Example 3: Verification of the online recursive convergence process:

[0329] This embodiment is used to demonstrate the convergence performance of the method of the present invention in a real online recursive calibration scenario.

[0330] Based on Example 1, the normalized input frequency is set to 0.3, and the SNR is set to 30dB. Using channel 0 as a reference, the actual timing deviations of channels 1, 2, and 3 are set to 20 ps, ​​-20 ps, ​​and 40 ps, ​​respectively. The initial estimates of the timing deviations for all channels are set to 0. The hybrid error term generated using the method of this invention... As the update direction, with a fixed step size Perform recursive updates using the LMS algorithm.

[0331] Implementation results are as follows Figure 5 As shown:

[0332] The horizontal axis represents the iteration number k, and the vertical axis represents the estimated time series deviation for each channel. As can be clearly seen from the graph, the estimated values ​​for the three channels start from an initial 0 ps and, with each iteration, monotonically and smoothly converge to near their respective true values, eventually reaching a stable state.

[0333] This embodiment demonstrates that the hybrid error term proposed in this invention can provide a stable update direction for LMS recursive updates, enabling the time series deviation estimate to converge stably during the iteration process and gradually approaching the true value. This shows that the method is suitable for online recursive estimation scenarios in multi-channel sampling systems.

[0334] The above description of several specific embodiments further details the technical solution provided by the present invention in order to highlight the advantages and benefits of the technical solution provided by the present invention. However, the above-described specific embodiments are not intended to limit the present invention. Any reasonable modifications and improvements to the present invention, reasonable combinations of embodiments, and equivalent substitutions based on the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A time series bias estimation method based on adaptive hybrid statistics, characterized in that, Applied to a multi-channel sampling system containing M channels, the method includes the following steps: Modeling steps: Obtain the output data of each channel of the multi-channel sampling system and establish an output model; the absolute timing deviation of each channel in the output model is the unknown parameter to be estimated; Conversion steps: The estimation objective of the output model is to estimate the absolute timing deviation of each channel, which is then converted into an estimate of the relative timing deviation between adjacent channels; Error compensation construction steps: For any pair of adjacent channels... and +1 is called the first For adjacent channels, based on their current time Relative timing deviation The estimated value Calculate to obtain the first For adjacent channels at the current time Compensation error ; Steps for generating complementary statistics: Based on the compensation error Parallel generation of correlation statistics Sum and difference statistics ; Statistical smoothing steps: For the correlation statistics... and the difference type statistic Smoothing was performed separately to obtain the smoothed correlation statistics. Smoothed difference statistic ; Adaptive weight calculation steps: Based on the aforementioned correlation statistics and the difference type statistic Calculate the smoothing error energy of the correlated path. Smoothing error energy of difference path Based on the two types of smoothing error energy and Calculate the adaptive fusion weights based on their relative size. This is to characterize the relative reliability of the two types of statistical paths, namely correlation and difference, at the current moment; Construction steps of the mixed error term: using the adaptive fusion weights The smoothed correlation statistics and the smoothed difference statistic Perform weighted fusion to construct a mixed error term The adaptive fusion weights Used to adjust the contribution ratio of the two types of statistical paths: correlation and difference. Timing bias update step: using the aforementioned mixed error term As the update direction, it drives the relative timing deviation estimate. Perform iterative updates; Result recovery and output steps: Based on the updated estimated relative timing deviation between adjacent channels after convergence. Recover and output the estimated absolute timing deviation values ​​for each channel. .

2. The time series deviation estimation method based on adaptive hybrid statistics according to claim 1, characterized in that, In the step of generating complementary statistics: The correlation statistics: ; The differential statistic is constructed from the sign information of the compensation error and the local slope, and is used to characterize the relationship between the direction of the compensation error and the local trend of signal change. ,in It is a symbolic function.

3. The time series deviation estimation method based on adaptive hybrid statistics according to claim 2, characterized in that, In the statistical smoothing step, a first-order infinite impulse response filter is used for smoothing. （8）； （9）； in, As a smoothing factor, .

4. The time series deviation estimation method based on adaptive hybrid statistics according to claim 3, characterized in that, The adaptive weight calculation step includes: Instantaneous energy calculation steps: Calculate the instantaneous average error energy: （14）； （15）； Energy smoothing step: Smooth the instantaneous average error energy: （16）； （17）； in, The energy smoothing factor is 0 < <1; Weight determination steps: Calculate the adaptive fusion weights: （18）。 5. The time series deviation estimation method based on adaptive hybrid statistics according to claim 4, characterized in that, In the step of constructing the mixed error term, the mixed error term Constructed using the following formula: 。 6. The time series deviation estimation method based on adaptive hybrid statistics according to claim 5, characterized in that, In the time-series deviation update step, the least mean square algorithm is used for iterative updates: ； in, This is the step size parameter.

7. The time series deviation estimation method based on adaptive hybrid statistics according to claim 1, characterized in that, The error compensation construction steps include: Calculate the local slope using backward difference: ； in, For the first Channel output; For the The output of channel +1 is compensated for first order: ； Calculate compensation error .

8. The time series deviation estimation method based on adaptive hybrid statistics according to claim 1, characterized in that, The result recovery and output steps include: The absolute timing deviation estimate of the reference channel is set to zero; Starting from the reference channel, the converged relative timing deviation estimates are sequentially accumulated to obtain the absolute timing deviation estimates for the remaining channels.

9. The time series deviation estimation method based on adaptive hybrid statistics according to any one of claims 1-8, characterized in that, The multi-channel sampling system is a time-interleaved analog-to-digital converter system.

10. A time series deviation estimation device based on adaptive hybrid statistics, characterized in that, For use in a multi-channel sampling system containing M channels, the device includes the following modules: Modeling module: acquires the output data of each channel of the multi-channel sampling system and establishes an output model; the absolute timing deviation of each channel in the output model is an unknown parameter to be estimated. Conversion module: The estimation objective of the output model is to estimate the absolute timing deviation of each channel, and to convert it into an estimate of the relative timing deviation between adjacent channels; Error compensation construction module: This module constructs any pair of adjacent channels. and +1 is called the first For adjacent channels, based on their current time Relative timing deviation The estimated value Calculate to obtain the first For adjacent channels at the current time Compensation error ; Complementary statistics generation module: based on the compensation error Parallel generation of correlation statistics Sum and difference statistics ; Statistical smoothing module: for the correlation statistics and the difference type statistic Smoothing was performed separately to obtain the smoothed correlation statistics. Smoothed difference statistic ; Adaptive weight calculation module: based on the aforementioned correlation statistics and the difference type statistic Calculate the smoothing error energy of the correlated path. Smoothing error energy of difference path Based on the two types of smoothing error energy and Calculate the adaptive fusion weights based on their relative size. This is to characterize the relative reliability of the two types of statistical paths, namely correlation and difference, at the current moment; Hybrid error term construction module: utilizing the adaptive fusion weights The smoothed correlation statistics and the smoothed difference statistic Perform weighted fusion to construct a mixed error term The adaptive fusion weights Used to adjust the contribution ratio of the two types of statistical paths: correlation and difference. Timing deviation update module: using the aforementioned mixed error term As the update direction, it drives the relative timing deviation estimate. Perform iterative updates; Result recovery and output module: Based on the updated estimated relative timing deviation between adjacent channels after convergence. Recover and output the estimated absolute timing deviation values ​​for each channel. .

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